Feeder grates, which are used as cooling grates or firing grates, consist alternately of stationary grate plates and transverse rows fo grate plates which can be moved forward and back in the feed direction. The rows of movable grate plates are supported, in total or in groups, by a movably mounted frame. Track rollers, which roll on a rail, are used for support. They are subject to high wear, which leads to an undesirable lowering of the movable grate plate rows relative to the stationary rows. It has been proposed (DE-C-38 44 493) to avoid this by support appliances which comprise a leaf spring on which the movable part of the grate is suspended so that it can oscillate. These support appliances have the disadvantage that the leaf springs must have a very long configuration so that the vertical component of the oscillating motion remains negligibly small. It is not only the space requirement associated with the great length of the leaf springs but also their large thermal expansion which causes difficulty. This thermal expansion leads to a lowering of the grate part and therefore affects the mutual positional relationship between the stationary and moving rows of grate plates.